Question 21

The surface area of the cube is 384 m squared.

To calculate the surface area of a cube, the formula is 6 times the square of the length of one edge. Given that each edge of the cube is 8 meters long, the surface area is calculated as 6 × (8 m)² = 6 × 64 m² = 384 m².

A) 384 m squared

This option is correct. The calculation of the surface area using the formula for a cube, 6 × (edge length)², confirms that with an edge length of 8 meters, the surface area is indeed 384 m².

B) 48 m squared

This option is incorrect. A surface area of 48 m² would imply that the edge length is much smaller than 8 meters, as per the formula for surface area. Specifically, if we calculate the edge length that would yield a surface area of 48 m², it would be significantly less than 8 meters, indicating a miscalculation.

C) 2304 m squared

This option is incorrect. A surface area of 2304 m² suggests an edge length that is far larger than the actual edge length of 8 meters. Using the surface area formula, this would imply an edge length of approximately 19.2 meters, which is not the case here.

D) 192 m squared

This option is incorrect. A surface area of 192 m² would also imply a different edge length. If we solve for the edge length that would give a surface area of 192 m², it would result in an edge length of approximately 8.0 meters, but this is inconsistent with the calculations based on the cube's actual dimensions.

Conclusion

The correct answer, 384 m², accurately reflects the surface area of the cube with edges of 8 meters. All other options miscalculate the relationship between edge length and surface area, demonstrating a misunderstanding of the formula required to derive the surface area of a cube. Hence, option A stands out as the only valid choice.